Question

The probability of simultaneous occurrence of at least one of two events A and B is \( p \). If the probability that exactly one of A, B occurs is \( q \), then \( P(A' \cup B') \) is equal to:

• A. \( 2 - 2p + q \)
• B. \( 2 + 2p - q \)
• C. \( 3 - 3p + q \)
• D. \( 2p - p + q \)

Hint:

Use the inclusion-exclusion principle to compute the probability of union and complements.

Answer 1

The Correct Option is A

Step 1: Use probability relationships.
We know that \( P(A \cup B) = P(A) + P(B) - P(A \cap B) \), and we can express \( P(A' \cup B') \) using the complement rule. Simplifying the equation gives \( 2 - 2p + q \).
Thus, the correct answer is (1).